Question: Rewrite as a simplified fraction. ${0.8\overline{1} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 81.1111...\\ 10x &= 8.1111...\end{align*}}$ Subtracting the two equations, we have: ${90x = 73}$ ${x = \dfrac{73}{90}} $